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Similarly, the Smilemore current account from internet bank Smile costs £10 a month but includes an interest-free overdraft up to £260 for the first year and pays an annual equivalent rate (AER) of 3.04pc gross on credit balances. It then adds worldwide family travel insurance, commission-free currency, Green Flag roadside assistance and ethical extras such as £25 off your first year's bill from green electricity company Ecotricity.

For £11.50 a month, Barclays' Additions Account provides perks including roadside assistance, mobile phone insurance, commission-free currency, a will-writing service and an identity theft advice helpline, all without needing to deposit a minimum amount each month.

There are currently 33 packaged account deals on the market, with average fees of around £11.50 a month, according to calculations by independent financial comparison website MoneyExpert.com.

However, Sean Gardner of MoneyExpert.com said: "Whether the First Direct move heralds the beginning of the end for free banking in the UK or whether it merely sparks greater interest in packaged accounts remains to be seen."

Susan Hannums, savings manager at AWD Chase de Vere, said: "I am not a big fan of packaged accounts. If you do your homework you'll realise they are just another sales tool that generate huge profits for the banks."

Indeed, Mr Gardner warns that many fee-free accounts offer better deals, on interest rates and overdraft charges for example, than packaged accounts with extras that are not used in the long term.

Ms Hannums said: "Anyone banking with First Direct should put their foot down on this one and move elsewhere. If First Direct gets away with it, they all will."